Related papers: From Geometry to Numerics: interdisciplinary aspec…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
The concept of boundary plays an important role in several branches of general relativity, e.g., the variational principle for the Einstein equations, the event horizon and the apparent horizon of black holes, the formation of trapped…
Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a…
This article translates some recent results on quasilocal horizons into the language of $(3+1)$ general relativity so as to make them more useful to numerical relativists. In particular quantities are described which characterize how…
The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\"{o}bner) methods are severely limited by algorithmic issues…
In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like…
The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general…
Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…
The astrophysics of compact objects, which requires Einstein's theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by…
Geometries with horizons offer insights into relationships between general relativity and quantum physics. For static spherically symmetric space-times, the event horizon is coincident with a coordinate anomaly that introduces complications…
The common intrinsic geometry shared by all the null hypersurfaces gives rise to the asymptotic symmetries found on the null infinities $\mathscr I^\pm$ and the isolated horizons $\Delta$. In this work, the properties of a null hypersurface…
Recent years have witnessed a rise in interest in the geometrical trinity of General Relativity and its extensions. This interest has been fuelled by novel insights into the nature of gravity, the possibility to address computational and…
I review recent results obtained for extensions of general relativity formulated within the Palatini formalism, an approach in which metric and connection are treated as independent geometrical entities. The peculiar dynamics of these…
Black holes represent extreme conditions of physical laws. Being predicted about a century ago, they are now accepted as astrophysical reality by most of the scientific community. Only recently more direct evidence of their existence has…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
In this paper we study several aspects of extremal spherical symmetric black hole solutions of four dimensional N=1 supergravity coupled to vector and chiral multiplets with the scalar potential turned on. In the asymptotic region the…
We carefully examine the exact analytic spectrum of quasinormal modes of general black holes in the so-called subtracted geometry of maximally supersymmetric supergravity. These black holes have the same area and surface gravity at both the…
The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory,…
The existence of black holes is a central prediction of general relativity and thus serves as a basic consistency test for modified theories of gravity. In spherical symmetry, only two classes of dynamic solutions are compatible with the…
In a two sided black hole, systems falling in from opposite asymptotic regions can meet inside the black hole and interact. This is the case even while the two CFTs describing each asymptotic region are non-interacting. Here, we relate…